Rigorous EUV mask simulator using 2D and 3D waveguide methods

Zhu, Zhengrong; Lucas, Kevin; Cobb, Jonathan; Hector, Scott Daniel; Strojwas, Andrzej J.

doi:10.1117/12.484963

Cited by 10 publications

(5 citation statements)

References 4 publications

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“…As opposed to the traditional T-matrix and robust Smatrix method, our approach first used the T-matrix method to obtain the "seed" matrix of two adjacent layers and then multiplied this seed matrix by itself several times to obtain the T-matrix of 64 repetitive and T-matrix of 16 repetitive reflective layers. These two T-matrices are going to be stitched into the discontinuous pattern layer into a S-matrix in order to prevent possible numerical overflow (5). This simulator was stable and matched published results obtained with other simulators (8).…”

Section: Introductionsupporting

confidence: 69%

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METROPOLE-3D: a three-dimensional electromagnetic field simulator for EUV masks under oblique illumination

et al. 2003

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Conventional lithography techniques have been losing their ability to easily support continuous shrinking of feature sizes, especially when the pattern half-pitch is <60 nm. EUV lithography is one of the leading contenders to replace these conventional techniques. Because the EUV mask structure is many times thicker than the illumination wavelength, scalar Fraunhofer diffraction calculations cannot describe the scattering of light from the EUV masks with enough accuracy.In this paper, we present a rigorous 3-D electromagnetic field simulator for EUV masks. The simulator is based on a 3-D waveguide method developed to calculate the characteristics of the light scattered from nonplanar EUV masks. A typical EUV mask contains as many as 80 reflective layers in addition to the absorbing layers, and we have developed a fast method to calculate the scattering matrix of the reflective layers. Also, based on the existing numerical techniques, we can describe the light scattering in the absorbing layers with complex index of refraction. The simulator has been recently modified to handle oblique illumination conditions, and this is the focus of our paper.Aerial images are calculated in the image plane of a typical EUV stepper, and a threshold resist model is used to predict the printed pattern size. We will first compare our work with published results on dense and isolated lines. Then, we will describe the results of our calculations for twodimensional patterns (e.g., contacts and islands) under oblique illumination. The typical simulation time is less than 10 hours on a desktop workstation for two-dimensional patterns.

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Section: Introductionsupporting

confidence: 69%

“…5. The highlight of that paper was a novel approach for stitching together the modes in the repetitive, uniform dielectric layers in the reflective mask.…”

Section: Introductionmentioning

confidence: 98%

METROPOLE-3D: a three-dimensional electromagnetic field simulator for EUV masks under oblique illumination

et al. 2003

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“…The model is based on the 2D spatial frequency solution to Maxwell's equations, the so-called waveguide method [17][18][19][20][21]. Firstly, the simulated structure is sliced into different rectangular layers with homogeneous optical properties in the Z-axis direction, as shown in Figure 4.…”

Section: Methodsmentioning

confidence: 99%

A 2D Waveguide Method for Lithography Simulation of Thick SU-8 Photoresist

et al. 2020

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Due to the increasing complexity of microelectromechanical system (MEMS) devices, the accuracy and precision of two-dimensional microstructures of SU-8 negative thick photoresist have drawn more attention with the rapid development of UV lithography technology. This paper presents a high-precision lithography simulation model for thick SU-8 photoresist based on waveguide method to calculate light intensity in the photoresist and predict the profiles of developed SU-8 structures in two dimension. This method is based on rigorous electromagnetic field theory. The parameters that have significant influence on profile quality were studied. Using this model, the light intensity distribution was calculated, and the final resist morphology corresponding to the simulation results was examined. A series of simulations and experiments were conducted to verify the validity of the model. The simulation results were found to be in good agreement with the experimental results, and the simulation system demonstrated high accuracy and efficiency, with complex cases being efficiently handled.

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“…Rigorous coupled wave analysis solves Maxwell's equations in the frequency domain, allowing for an efficient matrix algorithm to be used. 9,10 A vector model of propagation through the lens was assumed with random polarization of the illumination field at the mask. No condenser aberrations or intensity non-uniformity in the pupil were considered.…”

Section: Calculation Of σ Imagementioning

confidence: 99%

Evaluation of the critical dimension control requirements in the ITRS using statistical simulation and error budgets

2004

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To evaluate the ability to achieve the CD control requirements listed in the International Technology Roadmap for Semiconductors (ITRS) and to set error budget targets for focus, dose, PEB temperature uniformity, and mask CD control, statistical lithography simulation was used. A statistical model of total CD control, including the effects of intrafield and interfield error sources, was developed. The exposure tool settings such as wavelength, NA and partial coherence, focus and dose error budgets, lens aberration levels, mask type and pattern pitch values were determined for each node. Monte Carlo simulation was used to predict the CD error due to intrafield dose and focus errors. The contribution to CD error due to the mask was determined using mask CD control values in the ITRS and a calculated MEEF value at various defocus settings. The contribution to CD error due to PEB temperature variations, across wafer dose variations, and variation of aberrations and flare within the exposure field was also simulated. To meet ITRS CD control targets for 130-nm and 90-nm nodes, an alternating PSM mask is required along with a larger CD printed in resist than indicated in the ITRS. Meeting ITRS CD control requirements for 65-nm node and beyond not possible using assumptions detailed here, even with a near ideal APSM. The simulations predicted that if a relaxed pitch and a larger CD in resist were used at the 32nm node, 193nm immersion lithography in combination with a nearly ideal alternating PSM might provide CD control that is comparable to that obtainable using extreme ultraviolet lithography (EUVL).

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Rigorous EUV mask simulator using 2D and 3D waveguide methods

Cited by 10 publications

References 4 publications

METROPOLE-3D: a three-dimensional electromagnetic field simulator for EUV masks under oblique illumination

METROPOLE-3D: a three-dimensional electromagnetic field simulator for EUV masks under oblique illumination

A 2D Waveguide Method for Lithography Simulation of Thick SU-8 Photoresist

Evaluation of the critical dimension control requirements in the ITRS using statistical simulation and error budgets

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